Proverbs 25:20 What can I say?

²⁰ Like one who takes away a garment on a cold day,
    or like vinegar poured on a wound,
    is one who sings songs to a heavy heart.

I'll never forget the time that I was with a group of grieving family members who had experienced their loss within the last twenty-four hours, and hearing one of the extended family chirping cheerfully about how many times they'd experienced the same thing, and how everyone should just "buck up." 
That floored me.
Even Job's friends, who are criticized for their lack of understanding, waited with Job for seven days before they opened their mouths! (Check it out for yourself: Job 2:11-13)
In Romans, Paul gives advice that goes right along with Solomon's words:

Rejoice with those who rejoice, and weep with those who weep.  Romans 12:15

When you are suffering, and mourning, it seems there is a huge weight on top of you. In your mind, you know that "this too shall pass" and that if that person was a Christian, you will see them again. But your heart is heavy, because you loved and enjoyed that person's company -- and you can't experience that pleasure for a while now, till heaven. 
You are not yet ready to hear that "at least they are not in pain" or "they are in a better place" or that some good will come out of the situation.
And most of the time, the person who says, "I know just how you feel" really doesn't. Some do, of course, but too many mouth the words and don't really know.

Now, those are the negatives; let's look at what we can and should do:
As Christians, we need to be sensitive to the sufferings of others. The absolute best thing that we can do for a friend who is in grief is just . . . be there. Show your support by your quiet presence. Don't try to make things better, and don't, don't make light of that person's suffering. Sorrow and grief are complex processes that people have to go through --- it doesn't make them any less a Christian if they mourn and cry. Even though the pain they feel may never go completely away, it will change. It just takes time.
The time for talking will come. Comfort quietly first, and pray for them, that His peace will enfold them.